PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
80012^206892-11281762281Enzo Doria06/2014
8002(7*10^62278+113)/362279Robert Price10/2017
80033^130523+4662276Lelio R Paula04/2013
80042^206872-11345362275Enzo Doria07/2014
80052^206840-9362266Lelio R Paula08/2011
8006(1017*2^206815-1)/63562258Lelio R Paula04/2015
800796^31406+9562256Norbert Schneider03/2016
8008(2^206824+7)/64621362255Lelio R Paula03/2012
80092^206765-94168362243Paul Bourdelais11/2012
8010(6^79987-1)/562242Paul Bourdelais11/2007
80112^206755-157962240Yves Minet03/2013
801211^59764-582062238Enzo Doria01/2013
80135*10^62233+362234Dmitry Domanov11/2010
80148*3^130421+762228Lelio R Paula04/2014
801519^48661+1062226Lelio R Paula05/2013
8016(17*2^206705+1)/562225Lelio R Paula08/2012
80172^206705-11263562225Enzo Doria06/2014
80183^130403+868062219Lelio R Paula04/2013
801911^59740-711062213Enzo Doria01/2013
80212^206596-16762192Lelio R Paula08/2011
80202^206597+1891562192Lelio R Paula02/2013
80226^79918+13762189Lelio R Paula04/2013
8023lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
80242^206574+61362185Jason Earls04/2008
80253^130328+8062183Lelio R Paula04/2013
8026(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
80272^206550+7681962178Enzo Doria05/2016
802811^59703-2462175Lelio R Paula05/2013
80292^206524+7578162170Enzo Doria04/2016
80302^206506+42762165Henri Lifchitz01/2005
80312^206465+769562153Lelio R Paula02/2013
80322^206464-164962152Yves Minet03/2013
80335^88917+5662151Lelio R Paula04/2013
80342^206444-11156962146Enzo Doria05/2014
80355^88908-4262145Lelio R Paula04/2013
803618^49495-2962130Lelio R Paula05/2013
80373*6^79842-562130Lelio R Paula09/2014
80387*10^62127-1762128Robert Price01/2017
80392^206373+841562125Lelio R Paula02/2013
804020^47745-958362118Enzo Doria03/2013
804141^38516-262118Lelio R Paula08/2013
80422^206332-5869562113Lelio R Paula09/2011
804311^59639-126062108Enzo Doria11/2012
80442^206232-1589362083Enzo Doria04/2013
8045(115*10^62073-1)/362075Serge Batalov12/2014
80462^206206+7579962075Enzo Doria04/2016
8047(74*10^62072+43)/962073Robert Price10/2015
80482^206194-18562071Lelio R Paula08/2011
80496^79757-10362064Lelio R Paula04/2013
8050p(13285)#/2-6462063Robert Price04/2017
8051(29*10^62030-41)/362031Robert Price07/2016
805220^47675-8162027Lelio R Paula06/2013
80533^129972+9862013Lelio R Paula04/2013
80542^205962+362001Donovan Johnson02/2006
80552^205933-205933^261993Henri Lifchitz05/2005
8056(68*10^61991+7)/361993Robert Price03/2016
805720^47641-66361983Enzo Doria03/2013
80583^129861+266061960Lelio R Paula04/2013
8059(55459*2^205800+1)/134561954Lelio R Paula06/2014
806018^49354-9761953Lelio R Paula05/2013
8061(209*10^61947-17)/361949Robert Price05/2017
806214*10^61937+108961939Jens K. Andersen11/2007
8063(11*2^205758-1)/5361939Lelio R Paula01/2014
806420^47600+6361930Lelio R Paula06/2013
8065(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
806644117!3+24361918Robert Price09/2014
8067(31*2^205677-1)/5961915Lelio R Paula01/2014
8068(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
806920^47575-8161897Lelio R Paula06/2013
8070(58695*2^205593-1)/72761892Lelio R Paula04/2015
807187^31909+8661889Norbert Schneider10/2015
80722^205568+14161883Lelio R Paula08/2011
807310^61868+5892761869Patrick De Geest12/2012
807410^61868-3961868Robert Price05/2011
80765^88505-8861863Lelio R Paula04/2013
8075(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
807713^55528-9861856Lelio R Paula05/2013
8078(55^35543-1)/5461856Paul Bourdelais08/2017
807930535!2-861844Robert Price06/2015
808011^59371-120061829Enzo Doria11/2012
80817*2^205370-561824Lelio R Paula04/2014
8082(47*10^61821+403)/961822Robert Price04/2017
80832^205275+769561794Lelio R Paula02/2013
80842^205269+1291561793Lelio R Paula02/2013
8085(47*2^205265+1)/3561792Lelio R Paula04/2015
808619^48309+4061776Lelio R Paula05/2013
8087(424*10^61770-1)/961772Robert Price11/2017
80882^205192-407961769Yves Minet06/2011
80892^205184+1609561767Lelio R Paula09/2011
809020^47472-342361763Enzo Doria03/2013
8091(17*10^61760-89)/961761Robert Price11/2017
80922^205149-179561757Lelio R Paula09/2011
80932^205110-1761745Lelio R Paula08/2011
8094(373^24007+1)/37461737Eric Chen10/2017
8095(2^205025-7)/2561718Lelio R Paula03/2012
809627^43117-26^4311761717Robert Price08/2012
80972^205016+3761716Lelio R Paula08/2011
8098gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
80991263^19898+19898^126361712Serge Batalov05/2014
8100135^28963-13461701Norbert Schneider04/2015
8101(33*2^204966+1)/23434161698Michael Porter01/2015
8102(7*10^61696+167)/361696Robert Kinser10/2017
8103(46*10^61693+17)/961694Robert Price06/2015
8104((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+6676861684Phil Carmody09/2004
81051850^18879+18879^185061681Serge Batalov05/2014
81062^204891-100561679Lelio R Paula09/2011
8107151^28306-261679Lelio R Paula10/2017
8108(3^129271-5)/4150661674Lelio R Paula03/2012
810915937^7408+7408^1593761672Hans Havermann02/2017
81105^88216-1261661Lelio R Paula04/2013
811118185^2454+2454^1818561645Hans Havermann01/2017
81132^204767-1586561642Enzo Doria04/2013
8112(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
81147*2^204751-961638Lelio R Paula04/2014
81154*10^61625+2161626Robert Price08/2016
811615369^10226+10226^1536961626Hans Havermann02/2017
81172^204702-1812561622Enzo Doria05/2013
81185*3^129146+861620Lelio R Paula04/2014
81192^204673+12961613Lelio R Paula08/2011
812018^49079+9761608Lelio R Paula05/2013
8121106^30416+10561602Norbert Schneider12/2016
81222^204590-3361588Lelio R Paula08/2011
81232^204586-11197561587Enzo Doria06/2014
81242^204580-1607761585Enzo Doria04/2013
81252^204574-1604161583Enzo Doria04/2013
812615^52358+5661578Lelio R Paula05/2013
8127(28*10^61574+11)/361575Robert Price11/2015
81282^204516-1749361566Enzo Doria05/2013
81294*5^88076-361564Lelio R Paula09/2014
813011^59110-252061557Enzo Doria12/2012
81312^204477-5869561554Lelio R Paula09/2011
813212^57026-7361542Lelio R Paula05/2013
8133(257^25537+1)/25861541Richard Fischer04/2018
813417^50013+9061539Lelio R Paula05/2013
813556^35201-55^3520161538Robert Price10/2013
81368*7^72810+561533Lelio R Paula09/2014
8138204^26641-203^2664161531Jean-Louis Charton08/2009
813743867!3-656161531Robert Price11/2015
814110^61525+9^(61525-1)61526Robert Price03/2016
813910^61525+6225761526Patrick De Geest12/2016
814014821^14166+14166^1482161526Hans Havermann01/2017
814312^57010-8561525Lelio R Paula05/2013
814210^61525-21357961525Patrick De Geest12/2016
81442^204332-9961511Lelio R Paula08/2011
81452^204323-222161508Yves Minet08/2013
81472^204317-19561506Lelio R Paula08/2011
81463^128910-8661506Lelio R Paula04/2013
81482^204318+7453961506Enzo Doria04/2016
8149(2^204334-3)/114133361505Lelio R Paula03/2012
81502^204297-103609361500Paul Bourdelais11/2012
81513^128880+5861492Lelio R Paula04/2013
81522^204216-11167761476Enzo Doria05/2014
8153(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
81542^204129+20412961449Henri Lifchitz04/2002
81553^128787+2^(128787-1)61448Robert Price05/2016
815611^58999-7861442Lelio R Paula05/2013
81572^204083-11196761436Enzo Doria05/2014
8158(45^37159+1)/4661431Robert Price11/2013
8159677^21702+21702^67761430Norbert Schneider06/2016
816014837^13810+13810^1483761429Hans Havermann02/2017
8161(7*2^204043+1)/3961423Lelio R Paula03/2012
816211^58976-174061418Enzo Doria11/2012
81632^204016-1608561415Enzo Doria04/2013
8164V(379967)61393Serge Batalov03/2015
816543777!3-3^4377761392Robert Price08/2015
81667^72642+8861390Lelio R Paula04/2013
81673^128656+3261385Lelio R Paula04/2013
81682^203916-1749361385Enzo Doria05/2013
81696^78880+2361381Lelio R Paula04/2013
8170(388*10^61374-1)/961376Robert Price11/2017
81712^203877-11179961374Enzo Doria05/2014
81722^203867-161561371Lelio R Paula10/2011
81734*10^61367+1961368Robert Price04/2016
8174(19*2^203854+1)/4231961363Lelio R Paula08/2012
8175L(293659)/7652812271961361Serge Batalov07/2017
81762^203825-1580561358Enzo Doria04/2013
81772^203816-1582561355Enzo Doria04/2013
81785*10^61348+5961349Robert Price09/2016
817921^46395-261345Lelio R Paula08/2013
8180(809*29^41946-165)/2861344Curtis Bright05/2015
81817*6^78826+561340Lelio R Paula09/2014
8182(3^128558+7)/8377316642969661324Lelio R Paula04/2012
81832^203706-11161322Lelio R Paula08/2011
818417567^3094+3094^1756761318Hans Havermann02/2017
81852^203689-3161317Thomas Masser10/2005
8186(11*2^203678-1)/5368961310Lelio R Paula01/2014
81872^203642+3961303Lelio R Paula08/2011
8188floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
818911^58849-604061285Enzo Doria02/2013
819043694!3-361264Robert Price10/2014
819158*(10^(3*20420)-1)/111-161260Robert Price10/2014
81922^203490+1290961257Lelio R Paula10/2011
8193(16*10^61251-31)/361252Robert Price03/2016
819420^47077-570361249Enzo Doria03/2013
81952^203434-11308161240Enzo Doria07/2014
81975^87606+461234Wojciech Florek11/2005
81962^203412-16761234Lelio R Paula08/2011
81992^203402+108961231Lelio R Paula10/2011
8198(8*10^61230+67)/361231Robert Price01/2017
8200(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
82011265^19732+19732^126561211Serge Batalov05/2014
82022^203330+14561209Lelio R Paula08/2011
82036^78647-13761200Lelio R Paula04/2013
820485^31718+8461198Norbert Schneider10/2015
820511^58763-27061196Enzo Doria07/2012
82062^203285-11232161195Enzo Doria06/2014
82072^203253-99514361186Paul Bourdelais11/2012
820815319^9862+9862^1531961184Hans Havermann07/2016
82097^72395-4461181Lelio R Paula04/2013
8210(49*10^61167-67)/961168Robert Price08/2017
82115*2^203176-761163Lelio R Paula04/2014
8212(26*10^61156-413)/961157Robert Price10/2017
82147^72358+5461150Lelio R Paula04/2013
82132^203133-11177561150Enzo Doria05/2014
8215(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
82162^203112-1800961143Enzo Doria05/2013
821743607!3+72961129Robert Price09/2014
82182^203065-11485361129Enzo Doria05/2015
82193^128111+19661125Lelio R Paula04/2013
8220128^29007+29007^12861124Serge Batalov05/2014
82214*10^61119+4961120Robert Price08/2017
822222355*2^203009-361117Donovan Johnson03/2004
82232^203018+3361115Lelio R Paula08/2011
82242^203017-161561115Lelio R Paula10/2011
822516697^4570+4570^1669761110Hans Havermann12/2016
82262^202998-1724161109Enzo Doria05/2013
822720^46964+9361102Lelio R Paula06/2013
8228(55*10^61097-1)/961098Ray Chandler02/2012
822920^46960-546361097Enzo Doria03/2013
8230(11*10^61095+49)/361096Robert Price05/2016
82312^202934-595561090Lelio R Paula10/2011
823219^47772-6861089Lelio R Paula05/2013
82332^202877-49942361073Paul Bourdelais03/2013
82342^202763-1712561038Enzo Doria05/2013
8235(23*2^202756+1)/961037Lelio R Paula03/2012
823614788^13355+13355^1478861011Hans Havermann12/2016
823716069^6258+6258^1606961005Hans Havermann12/2016
82385^87276-1433661004Enzo Doria02/2013
823950^35899-49^3589960992Robert Price12/2012
82402^202599-304960989Yves Minet10/2014
82412^202535-11157160970Enzo Doria05/2014
8242(13*10^60966+107)/360967Robert Price11/2017
824410^60959+5760960Patrick De Geest12/2008
82436*10^60959-9160960Robert Price11/2017
824610^60959-6095960959Henri Lifchitz08/2002
824510^60959-2917760959Patrick De Geest08/2008
82475^87206+4^(87206+1)60955Robert Price07/2016
82482^202476-1590960952Enzo Doria04/2013
82492^202472-1751360951Enzo Doria05/2013
825014858^12651+12651^1485860950Hans Havermann12/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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